Manchester United were the luckiest team while Liverpool were the unluckiest in the whole Premier League last season, to the point where their table positions would have been flipped if not for luck, results of a research project show.

The Luck Index, designed and conducted by ESPN, Intel and the University of Bath, used a sophisticated predictive model and crunched hundreds of data points to discover how the 2017-18 Premier League table would look if adjusted for luck.

The study found that Manchester United (+0.25 lucky), who finished second behind champions Manchester City last year, would have finished with six fewer points on the season and landed in fourth place behind Liverpool and Tottenham.

The ESPN Luck Index

United were deemed lucky to beat Swansea on Aug. 19 and Brighton on Nov. 25, and to salvage a point at Liverpool on Oct. 14.

Conversely, the Luck Index showed Liverpool (-0.73 unlucky) would have earned a league-high 12 more points, moving them ahead of third-place Tottenham (whose total stayed the same) and United.

The study trained three reviewers who watched every game of the season and flagged incidents that could be considered lucky (and unlucky) in nine categories. Incidents were only included in the study if two of the three reviewers flagged an incident.

They came up with 157 incidents, of which a random sample of 20 were then ratified by a Premier League referee. They broke down as:

(Reviewers also checked for incorrectly awarded and converted free kicks, but no such incidents were included)

This dataset was then input into a predictive model that adjusted the final scores if those incidents had occurred differently -- accounting for the time of the incident, penalty conversion rates and more -- and output a probability density of scores across 100,000 simulations. The median probability (the most common) was then used to redraw the table.

Among the notable impacts on the final table:

-- Relegated Stoke City (-0.27) would have earned four more points, enough to move them from 19th place into 17th and send Huddersfield (-0.09) down in their place on goal difference. The Potters would have earned a win at Leicester on Feb. 24 and a draw against Crystal Palace on May 5.

-- Man City (-0.01) would have had only three points deducted from their 100 points -- still enough to break the previous Premier League record of 95. However, City benefitted from a league-high extra 13 goals, without which their record-breaking total of 106 would have been 93, well below the previous high of Chelsea's 103 from 2009-10. Their record plus-79 goal difference would have fallen to plus-66, below that same Chelsea squad's previous high of plus-71.

-- Arsenal's much-maligned away record in Arsene Wenger's final season would have been 11 points better, though the Gunners (-0.47) also benefited from an extra three points at home, for a net gain of eight points -- the second-most in the league that would have pushed them above Chelsea (-0.11) into fifth place.

-- Gary Cahill's sending off against Burnley in Chelsea's season opener was the only red card deemed to be given incorrectly all season.

-- Burnley, the second-luckiest team at +0.22, would still have been secure in their Europa League spot in seventh place despite dropping four points.

-- Leicester City's luck index of +0.20 slightly trailed Man United's +0.25, Burnley's +0.22 and Bournemouth's +0.21, but the Foxes benefitted the most in the table, earning seven extra points. Without that boost, they would have plummeted from ninth to 14th place. Bournemouth would have lost six points and fallen four spots to 16th.

-- Tottenham (-0.10) and Leicester were involved in the most incidents with 21, though Leicester's were more impactful, costing them seven goals and seven points in the table. Although Spurs would have lost 10 goals, their points total would not have moved.

-- Brighton's impressive return to the top flight would have been six points better, catapulting the Seagulls (-0.32) from 15th to a lofty ninth-place finish -- and an extra £12m in prize money.